The goals of this study are to establish the MTD for the administratin of a single IV bolus of cisplatin followed immediately by a 24-hour IV infusion of flavopiridol, and to determine the combined toxicities of flavopiridol and cisplatin. Although the single agent toxicities of flavopiridol and cisplatin appear to be mutually exclusive, it remains to be seen whether the combination will result in additional or augmented toxicities.